What is the Least Common Multiple of 75192 and 75200?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 75192 and 75200 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 75192 and 75200, than apply into the LCM equation.

GCF(75192,75200) = 8
LCM(75192,75200) = ( 75192 × 75200) / 8
LCM(75192,75200) = 5654438400 / 8
LCM(75192,75200) = 706804800

Least Common Multiple (LCM) of 75192 and 75200 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 75192 and 75200. First we will calculate the prime factors of 75192 and 75200.

Prime Factorization of 75192

Prime Factorization of 75200

Now multiplying the highest exponent prime factors to calculate the LCM of 75192 and 75200.

LCM(75192,75200) = 2⁶ × 3¹ × 13¹ × 241¹ × 5² × 47¹
LCM(75192,75200) = 706804800